In the scene on the balcony at the party, Miss Pettigrew eats the olive from her martini twice.
On the balcony, Miss Pettigrew is talking to Edythe. The two soldier extras behind Edythe are in the shot. Edythe switches places and the same two extras are in the shot on the other side of the balcony. As Edythe switches back to the first side, the same two extras enter the balcony from the sides she is on.
In the scene on the balcony at the party, Miss Pettigrew's martini changes from about one-third full to empty in an instant, just before Joe offers to refill it for her.
When Delysia Lafosse gets up from the bathtub, her right hand is covered in soap suds. In a close-up shot seconds later, the suds are gone.
When Joe sits down to speak to Miss Pettigrew in the nightclub, his cigarette changes from a tiny stub to almost one-third cigarette's length between shots.
In the scene where Delysia is telling Miss Pettigrew about her bit parts in the movies, she says she was "the one drinking the margarita," but the margarita wasn't invented until the 1940s.
The film takes place immediately before the outbreak of World War II, when England told Germany that they would declare war if Germany invaded Poland. Germany did so, and England declared war in early September, 1939. However, the film depicts an advanced state of autumn, with cool winds, dead leaves, etc. In actuality, war was declared on a beautiful late summer's day in England. It was not yet autumn.
Delysia is living in Nick's flat, but her name is on the plate outside the door. Nick, however, may only be paying for the flat and not living there.
In the closing scenes Miss Pettigrew is seen leaving the nightclub through a dressing room. The "WAY OUT" sign was probably Lexan with indirect lighting. Lexan was not invented until well after WWII and not in widespread use until the 1980s. However, similar signs made from plate glass with a slight green tint were made in the 20s if not earlier, so the sign as shown is in reality true to the era.
Johnny Mercer's Dream, a lovely song and fitting the mood of the scene, wasn't written until 1944.
The setting is pre-WWII. However, as Miss Pettigrew and Delysia are leaving the flat together, an iconic Honeywell round thermostat is seen on the wall behind them. This style of thermostat was not introduced until 1953.
At the big party, when Miss Pettigrew talks with Joe on the balcony, the boom mic is visible moving back and forth between characters in the reflection of the windows.
At Delysia's party, when Michael is playing the piano he leans into the higher notes toward screen right, from Michael's perspective, to the left. The higher keys on a piano are to the right, the lower to the left, so Michael's reaching to the left would result in lower notes.